Matrix Stiffness-Induced Transcriptome Alterations and Regulatory Mechanisms Revealed by RNA-Seq in Endothelial Cells

Changes in vascular stiffness are associated with the development and progression of many diseases, especially in cardiovascular disease. However, the effect of vascular stiffness on the endothelial cells (ECs) is not fully understood. Therefore, this study aims to determine the gene expression changes of ECs cultured on the matrices with different stiffness (1 kPa and 40 kPa, respectively) by RNA-seq, thereby broadening the knowledge between mechanics and biology. We obtained 1775 differentially expressed genes (DEGs) by RNA-seq, with 450 up-regulated and 1325 down-regulated DEGs in ECs cultured on soft matrix (1 kPa) compared to those cultured on stiff matrix (40 kPa). After that, we performed a series of functional enrichment analyses based on DEGs and found that DEGs were enriched in many signaling pathways like adhesion junction. Furthermore, transcription factor (TF) target gene prediction analysis and protein-protein interaction (PPI) analysis were also conducted. We found that mechanotransduction signaling related TFs such as BRD4 are involved in. And in the PPI analysis, some genes encoding extracellular matrix proteins such as fibronectin 1 (FN1) were identified as the hub genes. In order to confirm the RNA-seq results, we performed real-time qPCR analysis on the genes of interest, including FN1, collagen α2 (IV) chain, matrix metalloproteinase-14 and integrin α5, and found that the expression levels of all these genes were down-regulated on soft matrix, suggesting that soft matrix caused by pathological conditions may directly attenuate vascular barrier function. This study offers the insights about the effects of physical stimulation on cells, paving a way for vascular tissue engineering, regenerative medicine, disease modeling and therapies.

Activation of Piezo1 contributes to matrix stiffness-induced angiogenesis in hepatocellular carcinoma

Background:Despite integrin being highlighted as a stiffness-sensor molecule in matrix stiffness-driven angiogenesis,other stiffness-sensor molecules and their mechanosensory pathways related to angiogenesis in hepatocellular carcinoma(HCC)remain obscure.Here,we explored the interplay between Piezo1 and integrinβ1 in the mechanosensory pathway and their effects on HCC angiogenesis to better understand matrix stiffness-induced angiogenesis.Methods:The role of Piezo1 in matrix stiffness-induced angiogenesis was investigated using orthotopic liver cancer SD rat models with high liver stiffness background,and its clinical significance was evaluated in human HCC tissues.Matrix stiffness-mediated Piezo1 upregulation and activation were assayed using an in vitro fibronectin(FN)-coated cell culture system with different stiffness,Western blotting and Ca^(2+)probe.The effects of shPiezo1-conditioned medium(CM)on angiogenesis were examined by tube formation assay,wound healing assay and angiogenesis array.The underlying mechanism by which Piezo1 participated in matrix stiffness-induced angiogenesis was analyzed by microRNA quantitative real-time polymerase chain reaction(qRT-PCR),matrix stiffness measurement,dual-luciferase reporter assay,ubiquitination assay and co-immunoprecipitation.Results:Increased matrix stiffness significantly upregulated Piezo1 expression at both cellular and tissue levels,and high expression of Piezo1 indicated an unfavorable prognosis.High matrix stiffness also noticeably enhanced the activation level of Piezo1,similar to its expression level.Piezo1 knockdown significantly suppressed tumor growth,angiogenesis,and lung metastasis of HCC rat models with high liver stiffness background.shPiezo1-CM from HCC cells attenuated tube formation and migration abilities of vascular endothelial cells remarkably,and analysis of differentially expressed pro-angiogenic factors revealed that Piezo1 promoted the expression and secretion of vascular endothelial growth factor(VEGF),CXC chemokine ligand 16(CXCL16)and insulin-like growth factor binding protein 2(IGFBP2).Matrix stiffness-caused Piezo1 upregulation/activation restrained hypoxia inducible factor-1α(HIF-1α)ubiquitination,subsequently enhanced the expression of downstream pro-angiogenic factors to accelerate HCC angiogenesis.Besides,collagen 1(COL1)-reinforced tissue stiffening resulted in more expression of Piezo1 via miR-625-5p.Conclusions:This study unravels a new mechanism by which the inte-grinβ1/Piezo1 activation/Ca2+influx/HIF-1αubiquitination/VEGF,CXCL16 and IGFBP2 pathway participates in matrix stiffness-driven HCC angiogenesis.Simultaneously,a positive feedback regulation loop as stiff matrix/integrinβ1/miR-625-5p/Piezo1 and COL1/stiffer matrix mediates matrix stiffness-caused Piezo1 upregulation.

Matrix stiffness exacerbates the proinflammatory responses of vascular smooth muscle cell through the DDR1-DNMT1 mechanotransduction axis

Vascular smooth muscle cell (vSMC) is highly plastic as its phenotype can change in response to mechanical cues inherent to the extracellular matrix (ECM). VSMC may be activated from its quiescent contractile phenotype to a proinflammatory phenotype, whereby the cell secretes chemotactic and inflammatory cytokines, e.g. MCP1 and IL6, to functionally regulate monocyte and macrophage infiltration during the development of various vascular diseases including arteriosclerosis. Here, by culturing vSMCs on polyacrylamide (PA) substrates with variable elastic moduli, we discovered a role of discoidin domain receptor 1 (DDR1), a receptor tyrosine kinase that binds collagens, in mediating the mechanical regulation of vSMC gene expression, phenotype, and proinflammatory responses. We found that ECM stiffness induced DDR1 phosphorylation, oligomerization, and endocytosis to repress the expression of DNA methyltransferase 1 (DNMT1), very likely in a collagen-independent manner. The DDR1-to-DNMT1 signaling was sequentially mediated by the extracellular signal-regulated kinases (ERKs) and p53 pathways. ECM stiffness primed vSMC to a proinflammatory phenotype and this regulation was diminished by DDR1 inhibition. In agreement with the in vitro findings, increased DDR1 phosphorylation was observed in human arterial stiffening. DDR1 inhibition in mouse attenuated the acute injury or adenine diet-induced vascular stiffening and inflammation. Furthermore, mouse vasculature with SMC-specific deletion of Dnmt1 exhibited proinflammatory and stiffening phenotypes. Our study demonstrates a role of SMC DDR1 in perceiving the mechanical microenvironments and down-regulating expression of DNMT1 to result in vascular pathologies and has potential implications for optimization of engineering artificial vascular grafts and vascular networks.

Pathological matrix stiffness promotes cardiac fibroblast differentiation through the POU2F1 signaling pathway

Cardiac fibroblast(CF)differentiation into myofibroblasts is a crucial cause of cardiac fibrosis,which increases in the extracellular matrix(ECM)stiffness.The increased stiffness further promotes CF differentiation and fibrosis.However,the molecular mechanism is still unclear.We used bioinformatics analysis to find new candidates that regulate the genes involved in stiffnessinduced CF differentiation,and found that there were binding sites for the POU-domain transcription factor,POU2F1(also known as Oct-1),in the promoters of 50 differentially expressed genes(DEGs)in CFs on the stiffer substrate.Immunofluorescent staining and Western blotting revealed that pathological stiffness upregulated POU2F1 expression and increased CF differentiation on polyacrylamide hydrogel substrates and in mouse myocardial infarction tissue.A chromatin immunoprecipitation assay showed that POU2F1 bound to the promoters of fibrosis repressors IL1R2,CD69,and TGIF2.The expression of these fibrosis repressors was inhibited on pathological substrate stiffness.Knockdown of POU2F1 upregulated these repressors and attenuated CF differentiation on pathological substrate stiffness(35 kPa).Whereas,overexpression of POU2F1 downregulated these repressors and enhanced CF differentiation.In conclusion,pathological stiffness upregulates the transcription factor POU2F1 to promote CF differentiation by inhibiting fibrosis repressors.Our work elucidated the crosstalk between CF differentiation and the ECM and provided a potential target for cardiac fibrosis treatment.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE INCREMENT STIFFNESS MATRIX AND TOTAL QUANTUM STIFFNESS IN NONLINEAR ANALYSES

In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.

New Formula for Geometric Stiffness Matrix Calculation

The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

A New Modification to Shear Lag Model as Applied to Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

A new modification for the shear lag model is given and the expressions for the stiffness and yield Strength of short fiber metal matri×composite are derived. These expressions are then compared with our experimental data in a SiCw/Al-Li T6 composite and the published experimental data on different SiCw/Al T6 composites and also compared with the previous shear lag models and the other theoretical models.

ANALYSIS OF STRESS CONCENTRATIONS IN UNIDIRECTIONAL COMPOSITES TAKING INTO ACCOUNT THE TENSILE LOAD IN THE MATRIX

A modified shear-lag model accounting for the effect of the tensile stiffness of the ma, trix is proposed for solving the stress redistribution due to the failure of fibers and matrix in unidirectionally fibre-reinforced composites. The advantages of this model are simple, reasonable and accurate by comparison with the other similar modified shear-lag models. It can be further extended to study the stress redistribution with interfacial damage between fibres and matrix This paper quantitatively dis cusses the influence of the tensile stiffness ratio of matrix to fibre and of the fibre volume fraction on the stress concentration in the fibres and ma trix adjacent to cut fibres and matrix, and suggests that the influence of the matrix stiffness on the stress concentration can be neglected when the matrix stiffness is low, such as polymer matrix composites, and the fibre volume fraction is high. For other cases such as ceramic and metal matrix composites, the tensile load of the matrix cannot be neglected in the shear-lag analysis.

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

Topology Optimization of Stiffener Layout Design for Box Type Load-Bearing Component under Thermo-Mechanical Coupling

The structure optimization design under thermo-mechanical coupling is a difficult problem in the topology optimization field.An adaptive growth algorithm has become a more effective approach for structural topology optimization.This paper proposed a topology optimization method by an adaptive growth algorithm for the stiffener layout design of box type load-bearing components under thermo-mechanical coupling.Based on the stiffness diffusion theory,both the load stiffness matrix and the heat conduction stiffness matrix of the stiffener are spread at the same time to make sure the stiffener grows freely and obtain an optimal stiffener layout design.Meanwhile,the objectives of optimization are the minimization of strain energy and thermal compliance of the whole structure,and thermo-mechanical coupling is considered.Numerical studies for square shells clearly show the effectiveness of the proposed method for stiffener layout optimization under thermo-mechanical coupling.Finally,the method is applied to optimize the stiffener layout of box type load-bearing component of themachining center.The optimization results show that both the structural deformation and temperature of the load-bearing component with the growth stiffener layout,which are optimized by the adaptive growth algorithm,are less than the stiffener layout of shape‘#’stiffener layout.It provides a new solution approach for stiffener layout optimization design of box type load-bearing components under thermo-mechanical coupling.

A numerical framework for underground structures in layered ground under inclined P-SV waves using stiffness matrix and domain reduction methods

A numerical framework was proposed for the seismic analysis of underground structures in layered ground under inclined P-SV waves.The free-field responses are first obtained using the stiffness matrix method based on plane-wave assumptions.Then,the domain reduction method was employed to reproduce the wavefield in the numerical model of the soil–structure system.The proposed numerical framework was verified by providing comparisons with analytical solutions for cases involving free-field responses of homogeneous ground,layered ground,and pressure-dependent heterogeneous ground,as well as for an example of a soil–structure interaction simulation.Compared with the viscous and viscous-spring boundary methods adopted in previous studies,the proposed framework exhibits the advantage of incorporating oblique incident waves in a nonlinear heterogeneous ground.Numerical results show that SV-waves are more destructive to underground structures than P-waves,and the responses of underground structures are significantly affected by the incident angles.

UV-induced senescence of human dermal fibroblasts restrained by low-stiffness matrix by inhibiting NF-κB activation

As a hallmark of skin aging,senescent human dermal fibroblasts(HDFs)are known to lose the ability to divide.However,they can still interact with their cellular environment and the surrounding matrix.As the skin ages,the progressive slowing down of HDFs function decreases the skin’s structural integrity,which is more serious than if there is the dermal collagen matrix eroded.This leads to matters of the unbalanced barrier under the skin,skin fragility,inadequate wound healing,as well as other cosmetic issues.It is also well documented that skin aging comes with significant stiffness increases.Therefore,understanding the interactions between HDFs and the surrounding microenvironments during senescence may provide insights into skin aging.Here we aim to inves-tigate matrix stiffness’effect on HDF senescence and elucidate possible mechanisms that make HDFs senescent.In our experiments,HDFs were cultivated on Polydimethylsiloxane(PDMS)with various stiffnesses and exposed to UV light to trigger senescence.Results show that HDFs are significantly affected by senescence when cultured on a matrix with stiffness.However,the cells are not significantly affected when cultured on a low stiffness matrix.The following characterization revealed cells cultured on stiffsubstrates under UV exposure had stimu-lated the nucleus factor kappa-B(NF-κB)activation.In contrast,cells on a matrix of softness only displayed low activation of NF-κB.NF-κB activity suppression with ammonium pyrrolidine dithiocarbamate(PDTC)decreases UV-induced HDFs senescence on stiffsubstrates.Taken together,we demonstrated that soft matrix defends HDFs against ultraviolet-induced senescence by inhibiting the activation of NF-κB.

3D microgel with extensively adjustable stiffness and homogeneous microstructure for metastasis analysis of solid tumor

3D microgels with various mechanical properties have been important platforms tumor metastasis analysis,and widely adjustable stiffness is crucial for deeper researches.Herein,by mixing biodegradable polylactic acid(PLA)nanofibers in the modified alginate with different concentrations of Ca^(2+),we significantly enhance the stiffness range of microgels while retaining the pore size,which provides bionic microenvironment for tumor analysis.As a proof of concept,we simulated the mechanical characteristics of breast tumors by encapsulating cells in 3D microgels with diverse stiffness,and analyzed cellular behaviors of two typical breast cancer cell lines:MCF-7 and SUM-159.Results showed that with the addition of 2.0%(w/v)PLA short nanofibers,the Young’s modulus of modified alginate increased more than three-fold.Besides preserving high survival and proliferation rates,both cells also displayed stronger migration ability in soft microgel spheres,where RT-qPCR analysis revealed the underlying changes at the genetic level.This systematic study demonstrated our method is powerful for creating widely adjustable 3D mechanical microenvironment,and the results of cellular behavior analysis shows its promising application prospects in tumorigenesis and progression.

Substrate Stiffness and Topography Affect the Morphology of Human Fibroblasts in Mechanical Microenvironment

Hyperplastic scar is a common fibrotic disease that may ultimately lead to severe dysfunction anddeformity,causing physical and psychological distress.Therefore,we aim to evaluate the effect of the mechanicalmicroenvironment of scar substrates on the morphology of human fibroblasts(HFbs).The micro-modular fabrication technique was used to design a new cross-groove topology and to construct four elastic substrates withthe stiffness of 19.3 kPa and 90.1 kPa coupled with parallel groove and cross groove,respectively,to simulate themechanical microenvironment of skin wounds and scar tissues.The morphological changes in HFbs in differentsubstrates were observed,and the changes in the cell-long axis length,area,and the angle between cell-long axisand grooves were recorded.Immunofluorescence staining was performed to observe the distribution of microfilaments.The results indicated that substrate stiffness and topography affected the morphology of HFbs.The cellswere elongated in parallel grooves as well as in the area where cross grooves restricted groove length,the celllength was restricted,and the angle between the long axis and the groove was increased.The topography exertedno significant effect on the cell area,but the cell area increased with increasing the stiffness.The parallel groovepromoted the expression of the F-actin to a certain extent,and the fluorescence intensity of F-actin decreased withincreasing the stiffness.Studying the effect of the mechanical microenvironment of substrates on HFb morphologyis of great importance for understanding the mechanisms of scar formation and prevention.

DIRECT MANIPULATION OF B-SPLINE SURFACES

Engineering design and geometric modeling often require the ability to modifythe shape of parametric curves and surfaces so that their shape satisfy some given geometricconstraints, including point, normal vector, curve and surface. Two approaches are presented todirectly manipulate the shape of B-spline surface. The former is based on the least-square, whereasthe latter is based on minimizing the bending energy of surface. For each method, since unified andexplicit formulae are derived to compute new control points of modified surface, these methods aresimple, fast and applicable for CAD systems. Algebraic technique is used to simplify the computationof B-spline composition and multiplication. Comparisons and examples are also given.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Optimal Load Balancing Leveling Method for Multi-leg Flexible Platforms

The working platforms supported with multiple extensible legs must be leveled before they come into operation.Although the supporting stiffness and reliability of the platform are improved with the increasing number of the supporting legs,the increased overdetermination of the multi-leg platform systems leads to leveling coupling problem among legs and virtual leg problem in which some of the supporting legs bear zero or quasi zero loads.These problems make it quite complex and time consuming to level such a multi-leg platform.Based on rigid body kinematics,an approximate equation is formulated to rapidly calculate the leg extension for leveling a rigid platform,then a proportional speed control strategy is proposed to reduce the unexpected platform distortion and leveling coupling between supporting legs.Taking both the load coupling between supporting legs and the elastic flexibility of the working platform into consideration,an optimal balancing legs’ loads(OBLL) model is firstly put forward to deal with the traditional virtual leg problem.By taking advantage of the concept of supporting stiffness matrix,a coupling extension method(CEM) is developed to solve this OBLL problem for multi-leg flexible platform.At the end,with the concept of supporting stiffness matrix and static transmissibility matrix,an optimal load balancing leveling method is proposed to achieve geometric leveling and legs’ loads balancing simultaneously.Three numerical examples are given out to illustrate the performance of proposed methods.This paper proposes a method which can effectively quantify all of the legs’ extension at the same time,achieve geometric leveling and legs’ loads balancing simultaneously.By using the proposed methods,the stability,precision and efficiency of auto-leveling control process can be improved.